research.html0000644000175000017500000002370013674141263011673 0ustar mbrmbr research.utf8


Research interests

Publications & work in progress

“Median schemes for polygonal curvature flow,” in preparation

“Dirichlet puzzles,” in preparation

“Perron’s method for p-harmonious functions,” Electron. J. Differential Equations 2016, Paper No. 123 (with D. Hartenstine)

“Statistical exponential formulas for nonlinear diffusion,” Comm. Pure Applied Analysis 14 (2015), no. 1, pp. 269–284

“Statistical functional equations and p-harmonious functions,” Advanced Nonlinear Studies 13 (2013), no. 1, pp. 191–207 (with D. Hartenstine)

“Median values, 1-harmonic functions, and functions of least gradient,” Comm. Pure Applied Analysis 12 (2013), no. 2, pp. 711–719 (with H. Van Dyke)

“Asymptotic statistical characterizations of p-harmonic functions of two variables,” Rocky Mountain J. Math. 41 (2011), no. 2, pp. 493–504 (with D. Hartenstine)

“Positive symmetric solutions of singular semipositone boundary value problems,” E. J. Qualitative Theory of Diff. Equ., Spec. Ed. 1 (2009) No. 24, pp. 1–10 (with C. Tisdell)

“Existence and nonexistence results for quasilinear semipositone Dirichlet problems,” Electron. J. Differ. Equ. Conf. 17 (2009), pp. 207–212

“Radial solutions of quasilinear semipositone boundary-value problems,” Comm. Appl. Nonlinear Anal. 14 (2007), no. 1, pp. 113–119

“On the solvability of two-point, second-order boundary value problems,” Appl. Math. Lett. 20 (2007), no. 7, pp. 824–828 (with C. Tisdell)

“Game-theoretic schemes for generalized curvature flows in the plane,” Electron. J. Differ. Equ. Conf. 15 (2007), pp. 251–264

“Multiplicity results for semipositone problems on balls,” Dynam. Systems Appl. 15 (2006), no. 1, pp. 133–146 (with S. Robinson)

“Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds,” Dyn. Partial Differ. Equ. 2 (2005), no. 1, pp. 1–24 (with J. Nolen and J. Xin)

“A direct approach to Orlicz-Sobolev capacity,” Nonlinear Anal. 60 (2005), no. 1, pp. 129–147

“Weak and strong solvability of parabolic variational inequalities in Banach spaces,” J. Evol. Equ. 4 (2004), no. 4, pp. 497–517

“Solvability of nonautonomous parabolic variational inequalities in Banach spaces,” Differential Integral Equations 17 (2004), no. 9-10, pp. 1093–1122

Nonlinear Constrained Evolution in Banach Spaces, Ph.D. thesis, University of Utah, 2003

“Variational inequalities of elliptic and parabolic type,” Taiwanese J. Math. 6 (2002), no. 3, pp. 287–322 (with K. Schmitt)

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